Answer: length of B =4.00
Explanation:
for the vectors A and B and the angle between them as x.
Magnitude of the sum of A and B is given as = √(A²+B²+2ABcosx
where
Magnitude of A = 3.00
Magnitude of the sum of A and B is 5.00
5.00=√(A²+B²+2ABcos90°
5.00= √3² +b² +0
5²= 3² +b²
25=9+b²
b²= 25-9
b² = 16
b= √16
b= 4
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Answer:
78 km/h
Explanation:
If I normally drive a 12 hour trip at an average speed of 100 km/h, my destination has a total distance of:
- 100 km/h · 12 h = 1,200 km
Today, I drive the first 2/3 of the distance at 116 km/h. Let's first calculate what 2/3 of the normal distance is.
I've driven 800 km already. I need to drive 400 km more to reach my final destination. I need to figure out my average speed during this last 1/3 of the distance.
To do this, I first need to calculate how much time I spent driving 116 km/h for the past 800 km.
- 116 km/1 h = 800 km/? h
- 800 = 116 · ?
- ? = 800/116
- ? = 6.89655172
I spent 6.89655172 hours driving during the first 2/3 of the distance.
Now, I need to subtract this value from 12 hours to find the remaining time I have left.
- 12 h - 6.89655172 h = 5.10344828 h
Using this remaining time and my remaining distance, I can calculate my average speed.
- ? km/1 hr = 400 km/5.10344828 h
- 5.10344828 · ? = 400
- ? = 400/5.10344828
- ? = 78.3783783148
My average speed during the last third of the distance is around 78 km/h.
